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Prove that cos^(3)thetasin3theta+sin^(3)...

Prove that `cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 theta`.

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`cos^(3)thetaxxsin^(3)thetaxxcos 3 theta`
`=cos^(3)thetaxx(3sin theta-4 sin^(3)theta)+sin^(3)theta(4cos^(3)theta-3 cos theta)`
`=3cos^(3)thetasin theta-4 sin^(3)thetacos^(3)theta+4sin^(3)theta cos^(3)theta-3sin^(3)theta cos theta`
`=3 cos theta sin theta (cos^(2)theta-sin^(2)theta)`
`=(3)/(2)sin 2 theta cos 2 theta`
`=(3)/(4)sin 4 theta`.
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CENGAGE-TRIGONOMETRIC RATIOS AND TRANSFORMATION FORMULAS-Exercise 3.4
  1. tan(pi/4+theta)-tan(pi/4-theta)=2tan2theta

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  2. Prove that cosecA-2 cot 2A cos A=2sinA.

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  3. Prove that cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 ...

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  4. (sin^2 3A)/(sin^2A)-(cos^2 3A)/(cos^2A)=

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  5. Prove that (1+sec 2 theta)(1+sec 4 theta)(1+sec 8 theta)=(Tan 8theta)/...

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  6. If in an isosceles triangle with base 'a', vertical angle 20^@ and lat...

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  7. In DeltaABC, a = 3, b = 4 and c = 5, then value of sinA + sin2B + sin...

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  8. If cosA=3/4, then 32 sin, A/2 sin, (5A)/2= (A) sqrt(11) (B) -sqrt(11) ...

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  9. Find the value of (4cos^(2)9^(@)-1)(4cos^(2)27^(@)-1) (4cos^(2)81^(@...

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  10. If theta is an acute angle and sin((theta)/(2))=sqrt((x-1)/(2x)) ,then...

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  11. In a triangle ABC, if sin A sin(B-C)=sinC sin(A-B), then prove that co...

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  12. Let a=(pi)/(7), then (a) show that sin^(2)3a-sin^(2)a=sin2asin3a (...

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  13. Show that 1/(sin 10^@) - sqrt3/(cos 10^@) = 4

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  14. Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + co...

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  15. If tan x=(a)/(b) and tan 2x=(b)/(a+b) find the smallest positive value...

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  16. tantheta+tan(6 0^0+theta)+tan(12 0^0+theta)=3tan3theta

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  17. If A=110^(@), then prove that (1+sqrt(1+tan^(2)2A))/(tan2A)=-tan A.

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  18. If alpha and beta are the two different roots of equations alpha cos t...

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  19. If tan beta=cos theta tan alpha, then prove that tan^(2)""(theta)/(2)=...

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  20. If cos theta=a/(b+c), cos phi= b/(a+c) and cos psi=c/(a+b) where theta...

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